124 Quiz 2 Online Fall 2021 (2)
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MAT 124 Y01 Fall 2021
Name ______________________
Quiz 2 (3.3, 3.4, 6.1, 6.2 D and CI, 4.1) Grade is out of 38 points.
Directions
: Show all necessary work on paper, to be scanned and uploaded to the dropbox within the time limit. You may use StatKey but do not need Minitab. Use the formulas on the Reference Sheet to help you.
1) Given the original sample: 17, 10, 15, 21, 13, 18.
Circle the sample(s) below that constitute a possible bootstrap sample from the original sample.
a) 10, 12, 17, 18, 20, 21
b) 10, 15, 17
c) 10, 13, 15, 17, 18, 21
d) 18, 13, 21, 17, 15, 13, 10
e) 13, 10, 21, 10, 18, 17
[3 pts]
2) State the null and alternative hypotheses for the statistical test described.
Testing to see if there is evidence that a proportion is greater than 0.3.
H
0
:
[2 pts]
H
a
:
[2 pts]
3) Determine if each of the following have a sample statistic whose distribution is approximately normal. State a reason (or show some math) to support your answer.
(Remember for proportions, np ≥ 10 and n(1-p) ≥ 10, and for means n ≥ 30).
A: 163 out of 314 text messages sent by Prof. Congdon’s online Statistics students had no punctuation. B: The number of states visited by a group of 8 students are: 12, 6, 19, 5, 4, 5, 10, 49
[6 pts]
4) In Stat Key there is a data set in difference of means bootstrapping confidence intervals titled, Treadmill time (old versus young). This data set shows the time on the treadmill for old and young people. Here is a snapshot of the distribution with 3000 samples:
Based on what you see, could we use the 2 standard error rule for finding a 95% confidence interval? If yes, find the interval. If no, explain why. [8 pts]
5) In a sample of 800 adults in New York 480 chose Diet Pepsi over Diet Coke in a taste test. a) Using the formula approach and theoretical distribution, show the steps in constructing the 90% confidence interval estimate for the population proportion of adults in New York who prefer Diet Pepsi. Please show 3 decimal digits or more in your endpoints. [8 pts] b) Write an interpretation of your confidence interval. [3 pts]
6) What sample size is needed to give a margin of error within ±
0.5
in estimating a population mean with 99% confidence, if we make a reasonable estimate that σ
=
25
? [6 pts]
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